Squaring up in the fight to join Lord Nelson: cruise missiles, anti-war protesters and a hotel for pigeons

It was so much simpler in the 19th century. When Lord Nelson's statue was hauled to the top of its towering Corinthian column it was by public subscription to honour his "immortal memory".

In these less certain times, the question of who, or what, should join the great maritime hero in Trafalgar Square is one of glorious controversy.

Yesterday six artists shortlisted to create the next sculpture for the square's vacant fourth plinth revealed their ideas. Among their themes were pigeons, protesters and a woman with no arms.

The only uniting factor between the six maquettes - or models - which went on public display at the National Gallery yesterday was that traditionalists are likely to be offended, whoever is chosen.

None of the suggestions comes close to encapsulating the patriotic fervour of those who want a work that pays tribute to a national hero such as David Beckham or, at the very least, the late Queen Mother.

Sarah Lucas unveiled a car painted to look as if it was covered with pigeon droppings. The German artist Thomas Schütte continued the theme with Hotel for the Birds, which looks like a giant yellow, red and blue Perspex bird table.

Neither work is likely to delight Ken Livingstone, the Mayor of London, who has banned the selling of bird feed to cut the numbers of pigeons in the square.

More up his street - though still unlikely to impress Middle England - is Sokari Douglas Camp's tribute to the square's history of demonstrations, a 15ft-high tableau of anti-war protesters. Past protests, too, are evoked by Stefan Gec's life-size wooden Tomahawk cruise missiles, a modern take on Nelson and war.

Nelson was the inspiration for Marc Quinn, too, who echoes the leader's disability with a portrait of a woman with no arms. The final suggestion is a toy skyscraper reminiscent of New York's Twin Towers by Chris Burden.

Sandy Nairne, the director of the National Portrait Gallery who was asked by the Greater London Authority to chair the Fourth Plinth Commissioning Group, said they were "an inspiring range of ideas".

They were not looking for a permanent monument or memorial, Mr Nairne said, as the intention was for a rolling programme of temporary works following the trial commissions on the plinth four years ago.

But they had looked for art that reflected on the history and geography of the location. "We hope [these suggestions] will create a debate that reaches as many people as possible," he said. Debate is certain. David Lee, editor of Jackdaw magazine which is a cynical observer of the art scene, said he was not against the fourth plinth being used for modern sculpture.

"But we haven't got anybody who can do it. We're not very good at public art for the simple reason we have no system of communal belief," he said. "Anything to do with pigeons is a pathetic abnegation of real artistic responsibility and missiles are the kind of thing you would expect from an undergraduate."

He said he would probably plump for Burden. "He makes amazing bridge models that I rather like. There's no art to them but they're wonderful things," he said. "Sokari Douglas Camp is jolly but is not exactly gripping for such an imperial place."

Yet others were more enthusiastic. Derek Morris, president of the Royal Society of British Sculptors, said the whole scheme was "fantastic".

"My view, and I could probably say it was the society's view, is that what has been happening with the plinth has been a wonderful opportunity for contemporary sculpture to be part of the debate about what is good and what isn't in art. It's invigorating," he said. "It would be a shame to revert to putting up a statue commemorating somebody. I think in a way the traditional statue has sort of had its day.

"And we do have some of the best sculptors around in people like Antony Gormley and Rachel Whiteread. These figures are world-renowned."

It is a long time since the plinth was originally erected to house a commemorative statue. It was mounted for a statue of William IV, who left no money to pay for it. Neither was any forthcoming from the public and the plinth lay empty for 160 years. In the 1990s, Prue Leith, the cookery writer and deputy chairman of the Royal Society of Arts, decided something ought to be done, founded a committee and began asking people for their ideas.

The public suggested Nelson Mandela, Mahatma Gandhi, Diana, Princess of Wales and Shakespeare. The most popular suggestion was, apparently, the Queen Mother with three-time Grand National winner Red Rum. In the meantime, a series of temporary sculptures became a source of intrigue and controversy.

First came a statue of Christ by Mark Wallinger, later replaced by an allegorical bronze sculpture by Bill Woodrow showing a toppled human head, representing mankind, pressed down by a giant book representing knowledge and experience and bound to the roots of a tree.

Finally, Whiteread cast the plinth itself, then placed one on top of the other.

Wilfred Cass, the founder of the Goodwood Sculpture Park which helped choose and fund the first three temporary works, said they had clearly inspired many visitors to the park in West Sussex where the Woodrow work is now on permanent display.

"How many times in one's life does one get a chance to commission a piece of sculpture and have it standing in Trafalgar Square? It was amazing," Mr Cass said.

He said that he had been willing to continue funding the scheme but it was taken over by the mayor's office after Mr Livingstone was elected.

Now the Arts Council is paying £80,000 a year until 2005 to fund the maquettes and public consultation which will form part of the commissioning committee's decision-making. A recommendation for the first sculpture will be made in February and a sponsor will then be needed to fund the production.

Mr Cass said: "The public bodies said, 'We can't have a thing like Sculpture at Goodwood hogging this thing,' but now they have taken a year and half or two before anything will get on the plinth. It's a pity because there needed to be continuity. The question is who's going to pay for it?"

The funding issue leaves plenty of room for dispute even after the fireworks over selection have faded. In the meantime, the square is home to a bitter row over a separate work of art - the statue of Nelson Mandela which was originally proposed by the late South African newspaper editor Donald Woods and Sir Richard Attenborough and later taken up by Mr Livingstone and the Greater London Authority. The GLA submitted a planning application to Westminster council 18 months ago which remains unapproved.

An advisory panel, which includes representatives from the Tate, Royal College of Arts and National Gallery, rejected the proposal for a full-length bronze figure as not sufficiently high quality for the proposed site - in front of the Grade I listed National Gallery - or for the subject matter and repeated this advice to the council two weeks ago.

Yesterday, Mr Livingstone accused the Tories,who once supported the apartheid movement, of being behind the opposition to the statue. This was greeted with fury at Westminster where councillors demanded an immediate retraction.

It will not be the last row over sculpture in Trafalgar Square. Mr Lee has a soft spot for the plinth, alone and unadorned. "As a conceptual statement, I've always found it eloquent empty," he said.

THE BATTLE FOR TRAFALGAR SQUARE'S PLINTH

Chris Burden Toy Skyscraper as Tall as a Real Building

Burden is best known for his 2002 scale model of the Tyne Bridge constructed from Meccano for the opening exhibition of the Baltic contemporary art gallery in Gateshead. His piece for Trafalgar Square is almost seven metres high and was inspired by a full-size building. "I see this association as positive, as it will spark conversation about all structural, economic, safety and aesthetic issues involved in building structures that push towards the heavens," he said.

Sarah Lucas This One's for the Pigeons

Her work has been included in most new British art exhibitions. She is compiling an exhibition with Angus Fairhurst and Damien Hirst. The Ford Fiesta car is painted with resin and acrylic paint to give the appearance of being covered in pigeon dung ­ with London's pigeons then lending a hand. "[The work] highlights the everyday reality of the square and of this particular site with its casualness and humour," she said.

Marc Quinn Alison Lapper Pregnant

Quinn gained notoriety with his work Self (1991), a refrigerated cast of his head using nine pints of his blood. His piece for the square is a 4.7m white marble sculpture of a friend, Alison Lapper, when eight-and-a-half months pregnant. "In the past, heroes such as Nelson conquered the outside world. Now it seems they conquer their own circumstances and the prejudices of others, and I believe that Alison's portrait will symbolise this," he said.

Stefan Gec Mannequin

His work is rooted in his Ukrainian father's experience as a refugee during the Second World War. Thesetwo wooden life-size replicas of sea-launched Tomahawk cruise missiles use oak from Gloucestershire's Forest of Dean ­ the same used to construct the ships which fought at Trafalgar in 1805. "Ultimately Mannequin is a work that aims to explore the concept of victory and its commemoration in the 21st century," Gec said.

Sokari Douglas Camp No-o-War-r No-o-War-r

Camp has work on display in the new Sainsbury African Galleries at the British Museum. She said her piece, in stainless steel, aimed to celebrate and capture the diversity and energy of Londoners. She said: "My aim is to depict ordinary people as heroes ... These commemorate the ordinary sailors that fought in, and were the true heroes of, Nelson's campaigns."

Thomas Schütte Hotel for the Birds

He has exhibitions at many important international institutions including the DIA Centre for the Arts in New York and the Whitechapel Art Gallery. His offering in this instance is an architectural model in Perspex of yellow, red and blue which is able to have light reflecting through its edges and which stands five metres high. "[This sculpture] will become part of the important historical buildings all around Trafalgar Square ... a commentary on the present," he said.